Strength of Regression and Prediction

Please see the attached for instruction Strength of Regression and Prediction Instructions: Complete the following questions. Enter answers and explanations in this document. Show calculations in an Excel file, using a separate worksheet (tab) for each question. 1. A researcher is interested in sentencing dispositions and their relationship with the severity of a crime. She asked a sample of 10 prospective jury members to rate the seriousness of a particular crime (X) on a 1 (not very serious) to 7 (extremely serious) scale and then determine the sentence (Y) in years that sample members would recommend for that crime. The data are as follows: X Y 5 12 7 15 3 3 4 6 6 10 1 5 2 2 5 4 1 3 5 3 a. Calculate the regression slope and Y-intercept. Interpret your results. b. Predict the length of recommended sentence for a crime rated “5” on seriousness. c. Find the R-square. What does it mean? 2. A researcher has gathered data from seven randomly selected correctional employees on the number of years (X) the employees have worked in a particular department and their salaries (Y) in thousands of dollars. X Y 2 25.5 3 27 3 27.25 4 28.5 5 33 7 33 7 34.5 a. Calculate the regression slope and Y-intercept. Interpret your results. b. What would the predicted salary be for someone in the department who has worked for 6 years? c. Find the R-square. What does it mean? 3. A criminologist is interested in the effects of unemployment and policing on murder and has run the following multiple regression: Summary Output Regression Statistics Multiple R 0.90303 R Square 0.815462 Adjusted R Square 0.762737 Standard Error 5.11041 Observations 10 Coefficients Standard Error t Statistic P-value Intercept –23.26309588 7.075518018 –3.28783 0.013342 Unemployment rate 10.27754326 2.172859937 4.729961 0.002133 Police per 100,000 –0.046737101 0.023409765 –1.99648 0.086065 a. What is the Y-intercept? Interpret your results. b. Which variables are significant at the 0.05 level? c. What is the predicted homicide rate for a city with an unemployment rate of 5% and 250 police officers per 100,000 population?